Chemistry 4th Edition - (4 Atomic energy levels) PDF

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CHAPT ER 4

Atomic energy levels LEARNING OBJECT IVES After studying this chapter, you should be able to: 4.1 list some basic properties of atoms 4.2 explain the wave-like and particle-like properties of light, and how light interacts with atoms 4.3 describe the properties of electrons 4.4 explain the properties of bound electrons 4.5 describe orbitals in terms of electron distributions and energies 4.6 explain the structure of the periodic table in terms of electrons 4.7 write electron configurations 4.8 describe periodic trends in chemical and physical properties 4.9 describe periodic trends in relation to ions.

In the right combination, atoms and light combine to create one of the most remarkable tools of modern technology, the laser. Laser light is more highly organised than normal light. Laser light is monochromatic (has a single wavelength) and is highly directional, whereas conventional light sources typically produce light of many wavelengths. Figures 4.1a and 4.1b demonstrate these differences. In figure 4.1a, we see red laser light with wavelength of 650 nm pass through a prism.

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FIGURE 4.1

(a) Laser light consists of a single wavelength, whereas (b) white light consists of many wavelengths, and thus splits into its component colours when passed through a glass prism

(a)

Blackman, Allan. Chemistry, 4th Edition, Wiley, 2018. ProQuest Ebook Central, http://ebookcentral.proquest.com/lib/unsw/detail.action?docID=5561258. Created from unsw on 2021-05-30 23:39:14.

(b)

Although the light is refracted, there is no splitting into different colours, as we see for white light in figure 4.1b. This confirms that laser light consists of only one wavelength while normal white light comprises many wavelengths. Many of the applications of lasers take advantage of the high degree of organisation. Lasers are used in, for example, DVD scanners, eye surgery and fibre-optic communications. Lasers have also become versatile tools for scientific research. For example, finely tuned lasers have been used to deposit vapour-phase atoms on solid surfaces in regular patterns. The ability to manipulate individual atoms is likely to have important applications in nanotechnology. Every laser is based on the interactions between light and atoms or molecules. In this chapter, we describe the properties of atoms and light and the energy changes that accompany the interactions between them. Then we describe the properties of electrons bound to atoms and how these contribute to atomic structure. We explore the details of orbital energies and relate them to the ordering of atoms that leads to the familiar form and structure of the periodic table. Orbital energy levels have consequences that are far reaching, for example, they determine the stability and reactivity of atoms. The periodic table is based on orbital energy levels and provides the foundation for interpreting patterns of chemical behaviour related to an element’s position in the table.

4.1 Characteristics of atoms LEARNING OBJECTIVE 4.1 List some basic properties of atoms.

The atom is the fundamental building block of all matter. In this chapter, we will investigate the properties of atoms in some detail. We will start by outlining the basic characteristics of atoms; we read about many of these characteristics in the introductory chapter on the atom. Atoms possess mass, most of which is concentrated in the nucleus. The nucleus of an atom is small and positively charged, and all nuclei, except that of the hydrogen atom 1 H, consist of both positively charged protons and neutral neutrons. For neutral atoms, the positive charge of the nucleus is exactly balanced by negatively charged electrons; that is, a neutral atom contains equal numbers of protons and electrons. Atoms occupy volume, the majority of which is taken up by the electron cloud in the region of space around the nucleus. The chemical properties of elements are determined to a large extent by both their atomic size and their number of accessible (valence) electrons. Finally, atoms can attract one another and, as a result, can combine to form, for example, molecules. This chapter examines in detail how both the number of electrons and their specific arrangement influence chemical properties. Light is an essential tool for probing the properties of electrons and since there are similarities between the properties of light and electrons, we will begin our discussion by describing the properties of light and its interaction with atoms.

4.2 Characteristics of light Copyright © 2018. Wiley. All rights reserved.

LEARNING OBJECTIVE 4.2 Explain the wave-like and particle-like properties of light, and how light interacts with atoms.

The most useful tool for studying the structure of atoms is electromagnetic radiation. What we call light is one form of this radiation, with other forms including radiowaves, microwaves and X-rays. We need to know about the fundamental properties of light to understand what electromagnetic radiation reveals about atomic structure.

CHAPT ER 4 Atomic energy levels 165

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Wave-like properties of light Light has wave-like properties. A wave is a regular FIGURE 4.2 A light wave can be described by its oscillation in some particular property, such as the upwavelength or frequency. As and-down variation in position of water waves. Water wavelength increases, frequency waves vary with time. A surfer waiting for a ‘big one’ decreases, and vice versa. bobs up and down as ‘small ones’ pass by. Light waves 1 second vary with time too, in a more regular manner than water waves. This variation is characterised by the wavelength, λ wave’s frequency (𝝂), which is the number of wave v = 4 s‒1 (4 Hz) crests passing a point in space in 1 second (so the unit amplitude is s−1 , also designated hertz or Hz). Water waves also vary in height as you move away from the beach; that is, the height of the wave varies with position. Light waves vary in space in a manner illustrated in figure 4.2. This variation in space is characterised by the wavelength (𝝀), which is the distance between successive wave crests. Wavelengths are measured in units of λ v = 8 s‒1 (8 Hz) length, such as metres or nanometres. As we will see below, frequency and wavelength are not independent variables, but are inversely proportional to each other. Amplitude is the maximum displacement of a wave from its centre. The amplitude of a light wave determines the intensity of the light. As figure 4.3 illustrates, a bright light is more intense than a dim one as its waves have higher amplitudes. It is important λ v = 16 s‒1 (16 Hz) to note that the intensity of light is proportional to the square of its amplitude. The amplitude itself has no physical meaning because at any moment in time the amplitude of the wave can be negative or positive, while the square is always positive and equivalent to photon density. Waves can also be described in terms of their phase. Phase refers to the starting position of a wave with respect to one wavelength. We can see that waves in figures 4.4a and 4.4b have the same amplitude and wavelengths, but different starting points. We say that the two waves have different phases. We can see this more clearly in figure 4.4c, which shows the two waves superimposed. If they had the same phase (and the same amplitude and wavelength), they would line up perfectly. When two waves interact, the outcome is influenced, among other things, by their relative phases. The amplitudes of both waves will be added, which in the example in figure 4.4 would lead to exact cancellation. Light waves, and all other types of electromagnetic radiation, always move through a vacuum at the same speed. The speed of light is a fundamental constant c = 2.997 924 58 × 108 m s−1 (we will round it to 2.998 × 108 m s −1 ). For any wave, its frequency (v) (in units of s−1 ) multiplied by its wavelength (𝜆) (in units of m) equals its speed c (m s−1 ), that is: c = v𝜆

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The amplitude of a light wave determines the intensity of the light. A bright light is more intense, that is, has a higher amplitude, than a dim light.

FIGURE 4.3

higher amplitude 2

2

1

1

lower amplitude dim light

bright light

‒1

‒1

‒2

FIGURE 4.4

wavelength

‒2

wavelength

Phase refers to the starting position of a wave with respect to one wavelength. The waves in (a) and (b) have different phases; (c) shows an overlap of (a) and (b).

(a)

(b)

(c)

WORKED EXAMPLE 4.1

Wavelength–frequency conversion An FM radio station transmits its signal at 103.4 MHz. What is the wavelength of the signal? Analysis The link between wavelength (𝜆) and frequency (v) is given by c = v𝜆. Solution First, we summarise the data.

c = 2.998 × 108 m s−1

v = 103.4 MHz

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Next, we rearrange the equation to solve for wavelength.

c = v𝜆 so

𝜆=

c v

To obtain equivalent units, convert the frequency units from MHz to Hz. The prefix ‘M’ stands for ‘mega’, which is a factor of 106 . Remember that Hz is equivalent to s−1 .

𝜆=

2.998 × 108 m s−1 = 2.90 m 103.4 × 106 s−1

Is our answer reasonable? The wavelength of 2.90 m may seem rather long, but radio waves are known as long wavelength radiation. See figure 4.5 for a sense of the wavelengths of electromagnetic radiation.

CHAPT ER 4 Atomic energy levels 167

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PRACTICE EXERCISE 4.1

What is the frequency of electromagnetic radiation that has a wavelength of 1.40 cm?

The wavelengths or frequencies of electromagnetic radiation cover an immense range. Figure 4.5 shows that the visible spectrum covers the wavelength range from about 380 nm (violet) to 780 nm (red). The centre of this range is yellow light, with a wavelength of about 580 nm and a frequency around 5.2 × 1014 s−1 . Although visible light is extremely important to living creatures for vision, the whole electromagnetic spectrum from gamma rays to radio waves also has diverse effects on, and uses in, our lives. FIGURE 4.5

The electromagnetic spectrum, showing its various regions and the associated wavelengths and frequencies

X-ray

sun lamps

heat lamps

frequency, v (Hz) 1020 gamma rays 10‒12

1018

1016

10‒10

1014

ultraviolet

X-rays

microwave ovens, police radar, satellite stations 1012

infrared

10‒8

10‒6

UHF TV, mobile phones

1010

108

microwaves radar

10‒4

FM radio, VHF TV

visible spectrum

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4.0

4.5

5.0

5.5

6.0

106

104

TV, FM AM long radio radio waves waves

100

10‒2

AM radio

102

104

wavelength, λ (m)

6.5

7.0

7.5

(10‒7 m)

Radiation with short wavelengths, in the X-ray and gamma ray regions, can generate ions by removing electrons from atoms and molecules. These ions are highly reactive and can cause serious damage to the material that absorbs the radiation. However, under closely controlled conditions, X-rays are used in medical imaging, and gamma rays are used to treat cancer. The wavelength of ultraviolet (UV) radiation lies between that of X-rays and visible light. Ultraviolet radiation can also damage materials, especially in high doses. High rates of skin cancer in Australia and New Zealand are a direct result of exposure to damaging UV radiation in sunlight. Radiation with long wavelengths falls in the infrared, microwave or radio frequency regions. Heat lamps make use of infrared radiation, microwave ovens cook with microwave radiation, and radio and television signals are transmitted by radio waves. What we perceive as white light actually contains a range of wavelengths. This becomes apparent when white light passes through a prism (see figure 4.1b) or through water droplets, which creates a rainbow. These objects refract different wavelengths of light through different angles, so the light that passes through spreads out in space, with each wavelength appearing at its own characteristic angle.

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Particle properties of light Light carries energy. When our bodies absorb sunlight, for example, we feel warm because energy from the sunlight has been transferred to our skin. A phenomenon known as the photoelectric effect shows how the energy of light depends on its frequency and intensity. The photoelectric effect is the basis for many light-sensing devices, such as automatic door openers and camera exposure meters. Figure 4.6 illustrates a photoelectric experiment in which a beam of light strikes the surface of a metal. Under the right conditions, the light causes electrons to be ejected from the metal surface. A detailed study of the photoelectric effect reveals how the behaviour of these electrons is related to the characteristics of light. 1. Below a characteristic threshold frequency, v0 , no electrons are observed, regardless of the light’s intensity. 2. Above the threshold frequency, the maximum kinetic energy of ejected electrons increases linearly with the frequency of the light, as shown in figure 4.7. Kinetic energy is a function of the electron’s speed. We will learn more about kinetic energy in the chapter on gases. 3. Above the threshold frequency, the number of emitted electrons increases with the light’s intensity, but the kinetic energy per electron does not depend on the light’s intensity. 4. All metals exhibit the same behaviour, but, as figure 4.7 indicates, each metal has a different threshold frequency. FIGURE 4.6

A diagrammatic view of the photoelectric effect. When light of a high enough frequency strikes a metal, electrons are ejected from the surface.

light metal surface

detector electrons current meter

+

‒ vacuum chamber

+ ‒ voltage voltage source source

In this equation, E is the energy of a photon of light and v is its frequency. The proportionality constant between energy and frequency is known as Planck’s constant (h) and has a value of 6.626 069 57(29) × 10−34 J s (we will use 6.626 × 10−34 J s). The 29 in parentheses refers to the uncertainty in the final digits; therefore, h = (6.626 069 57 ± 0.000 000 29) × 10−34 J s.

FIGURE 4.7

Variation in the maximum kinetic energy of electrons ejected from two different metal surfaces (a and b) as a function of the frequency of incoming light

Kinetic energy of ejected electrons

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In 1905, Albert Einstein postulated that light comes in ‘packets’ or ‘bundles’, called photons. Each photon has an energy that is directly proportional to its frequency. Ephoton = hvphoton

a

v0a

b

v0b Frequency of light, v

CHAPT ER 4 Atomic energy levels 169

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WORKED EXAMPLE 4.2

The energy of light What is the energy of a photon of blue light with a wavelength of 475 nm? Analysis This conversion problem requires two steps. We do not have an equation that will calculate E based on the data we have, but, by combining the two equations we do know, we can relate the energy of a photon to its frequency and wavelength. Solution We summarise the data.

h = 6.626 × 10−34 J s

c = 2.998 × 108 m s−1

𝜆 = 475 nm

We combine the equations into an equation that relates energy to wavelength.

E = hv and

v=

c 𝜆

so

E=

hc 𝜆

Substituting our data, we find:

Ephoton =

(6.626 × 10−34 J s)(2.998 × 108 m s−1 )

475 × 10−9 m −1 s✚ ) m✚ (6.626 × 10−34 J s)(2.998 × 108 ✚ ✄ = 475 × 10−9 ✚ m = 4.18 × 10−19 J

Is our answer reasonable? An energy of 10−19 J seems very small, but we must remember that this is the energy of a single photon. If we want to calculate the energy of 1 mol of these photons, we need to multiply our result by the Avogadro constant.

E1 mol of photons = Ephoton × NA = (4.18 × 10−19 J) × (6.022 × 1023 mol−1 ) = 251 × 103 J mol−1 = 251 kJ mol−1 This energy is comparable to the energies of chemical bonds.

PRACTICE EXERCISE 4.2

What is the energy of a photon with a wavelength of 254 nm (UV radiation)?

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Einstein concluded that the energy of a photon that has the threshold frequency (v0 ) corresponds to the binding energy of the electron. Energy beyond the threshold frequency increases the electron’s kinetic energy as shown in figure 4.8. This can be described by: electron kinetic energy = photon energy − binding energy Ekinetic(electron) = hv − hv0 Einstein’s explanation accounts for the observed properties of the photoelectric effect. When the energy of the photon is less than hv0 (low-frequency light), no electrons can escape from the metal surface, no matter how intense the light. When the energy of the photon is greater than hv0 , an electron is ejected and any excess energy is transferred to that electron as kinetic energy. The intensity of a light beam is a measure of the number of photons per unit time; light of a higher amplitude carries more photons than light of lower amplitude. The intensity of the light does not determine the amount of energy per photon. More photons striking the metal result in more electrons being ejected, but the energy of each photon and 170 Chemistry

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FIGURE 4.8

Diagram of the energy balance for the photoelectric effect

Ekinetic

Energy

each electron is unchanged. Finally, the fact that each metal has its own characteristic threshold frequency suggests that electrons are bound more tightly to some metals than to others. Einstein’s explanation of the photoelectric effect showed that light has some properties of particles. A complete description of light includes both wave-like and particle-like properties. When light interacts with a relatively large body such as ...